2(5x+2)10x=4

Solution for 2(5x+2)10x=4 equation:

2(5x+2)10x=4

We move all terms to the left:

2(5x+2)10x-(4)=0

We multiply parentheses

100x^2+40x-4=0

a = 100; b = 40; c = -4;
Δ = b2-4ac
Δ = 402-4·100·(-4)
Δ = 3200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40\sqrt{2}}{2*100}=\frac{-40-40\sqrt{2}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40\sqrt{2}}{2*100}=\frac{-40+40\sqrt{2}}{200}
$